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NASA NTRS2004

Theoretical Astrophysics at Fermilab

The Theoretical Astrophysics Group works on a broad range of topics ranging from string theory to data analysis in the Sloan Digital Sky Survey. The group is motivated by the belief that a deep understanding of fundamental physics is necessary to explain a wide variety of phenomena in the universe. During the three years 2001-2003 of our previous NASA grant, over 120 papers were written; ten of our postdocs went on to faculty positions; and we hosted or organized many workshops and conferences. Kolb and collaborators focused on the early universe, in particular and models and ramifications of the theory of inflation. They also studied models with extra dimensions, new types of dark matter, and the second order effects of super-horizon perturbations. S tebbins, Frieman, Hui, and Dodelson worked on phenomenological cosmology, extracting cosmological constraints from surveys such as the Sloan Digital Sky Survey. They also worked on theoretical topics such as weak lensing, reionization, and dark energy. This work has proved important to a number of experimental groups [including those at Fermilab] planning future observations. In general, the work of the Theoretical Astrophysics Group has served as a catalyst for experimental projects at Fennilab. An example of this is the Joint Dark Energy Mission. Fennilab is now a member of SNAP, and much of the work done here is by people formerly working on the accelerator. We have created an environment where many of these people made transition from physics to astronomy. We also worked on many other topics related to NASA s focus: cosmic rays, dark matter, the Sunyaev-Zel dovich effect, the galaxy distribution in the universe, and the Lyman alpha forest. The group organized and hosted a number of conferences and workshop over the years covered by the grant. Among them were:

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NASA NTRS1991

Nano-G research laboratory for a spacecraft

An acceleration free research laboratory is provided that is confined within a satellite but free of any physical engagement with the walls of the satellite, wherein the laboratory has adequate power, heating, cooling, and communications services to conduct basic research and development. An inner part containing the laboratory is positioned at the center-of-mass of a satellite within the satellite's outer shell. The satellite is then positioned such that its main axes are in a position parallel to its flight velocity vector or in the direction of the residual acceleration vector. When the satellite is in its desired orbit, the inner part is set free so as to follow that orbit without contacting the inside walls of the outer shell. Sensing means detect the position of the inner part with respect to the outer shell, and activate control rockets to move the outer shell; thereby, the inner part is repositioned such that it is correctly positioned at the center-of-mass of the satellite. As a consequence, all disturbing forces, such as drag forces, act on the outer shell, and the inner part containing the laboratory is shielded and is affected only by gravitational forces. Power is supplied to the inner part and to the laboratory by a balanced microwave/laser link which creates the kind of environment necessary for basic research to study critical phenomena such as the Lambda transition in helium and crystal growth, and to perform special metals and alloys research, etc.

Vonbun, Friedrich O.↗

NASA NTRS2012

Future Gamma-Ray Imaging of Solar Eruptive Events

Solar eruptive events, the combination of large solar flares and coronal mass ejections (CMEs), accelerate ions to tens of Gev and electrons to hundreds of MeV. The energy in accelerated particles can be a significant fraction (up to tens of percent) of the released energy and is roughly equipartitioned between ions and electrons. Observations of the gamma-ray signatures produced by these particles interacting with the ambient solar atmosphere probes the distribution and composition of the accelerated population, as well as the atmospheric parameters and abundances of the atmosphere, ultimately revealing information about the underlying physics. Gamma-ray imaging provided by RHESSI showed that the interacting approx.20 MeV/nucleon ions are confined to flare magnetic loops rather than precipitating from a large CME-associated shock. Furthermore, RHESSI images show a surprising, significant spatial separation between the locations where accelerated ions and electrons are interacting, thus indicating a difference in acceleration or transport processes for the two types of particles. Future gamma-ray imaging observations, with higher sensitivity and greater angular resolution, can investigate more deeply the nature of ion acceleration. The technologies being proven on the Gamma-Ray Imager/Polarimeter for Solar flares (GRIPS), a NASA balloon instrument, are possible approaches for future instrumentation. We discuss the GRIPS instrument and the future of studying this aspect of solar eruptive events.

Shih, Albert↗

NASA NTRS1999

Space Acceleration Measurement System for Free Flyers

Experimenters from the fluids, combustion, materials, and life science disciplines all use the microgravity environment of space to enhance their understanding of fundamental physical phenomena caused by disturbances from events such as spacecraft maneuvers, equipment operations, atmospheric drag, and (for manned flights) crew movement. Space conditions reduce gravity but do not eliminate it. To quantify the level of these disturbances, NASA developed the Space Acceleration Measurement System (SAMS) series to collect data characterizing the acceleration environment on the space shuttles. This information is provided to investigators so that they can evaluate how the microgravity environment affects their experiments. Knowledge of the microgravity environment also helps investigators to plan future experiments. The original SAMS system flew 20 missions on the shuttle as well as on the Russian space station Mir. Presently, Lewis is developing SAMS-II for the International Space Station; it will be a distributed system using digital output sensor heads. The latest operational version of SAMS, SAMS-FF, was originally designed for free flyer spacecraft and unmanned areas. SAMS-FF is a flexible, modular system, housed in a lightweight package, and it uses advances in technology to improve performance. The hardware package consists of a control and data acquisition module, three different types of sensors, data storage devices, and ground support equipment interfaces. Three different types of sensors are incorporated to measure both high- and low-frequency accelerations and the roll rate velocity. Small, low-power triaxial sensor heads (TSH's) offer high resolution and selectable bandwidth, and a special low-frequency accelerometer is available for high-resolution, low-frequency applications. A state-of-the-art, triaxial fiberoptic gyroscope that measures extremely low roll rates is housed in a compact package. The versatility of the SAMS-FF system is shown in the three different types of missions SAMS-FF has supported.

Kacpura, Thomas J.↗

NASA NTRS1994

A new path for the electron bulk energization in solar flares: Fermi acceleration by magnetohydrodynamic turbulence in reconnection outflows

We recently proposed that a magnetohydrodynamic (MHD) turbulent cascade produces the bulk energization of electrons to approximately 25 keV in the impulsive phase of solar flares (LaRosa & Moore 1993). In that scenario, (1) the cascading MHD turbulence is fed by shear-unstable Alfvenic outflows from sites of strongly driven reconnection in the low corona, and (2) the electrons are energized by absorbing the energy that flows down through the cascade. We did not specify the physical mechanism by which the cascading energy is ultimately transferred to the electrons. Here we propose that Fermi acceleration is this mechanism, the process by which the electrons are energized and by which the cascading MHD turbulence is dissipated. We point out that in the expected cascade MHD fluctuations of scale 1 km can Fermi-accelerate electrons from 0.1 keV to approximately 25 keV on the subsecond timescales observed in impulsive flares, provided there is sufficient trapping and scattering of electrons in the MHD turbulence. We show that these same fluctuations provide the required trapping; they confine the electrons within the turbulent region until the turbulence eis dissipated. This results in the energization of all of the lectrons in each large-scale (5 x 10(exp 7)cm) turbulent eddy to 25 keV. The Fermi process also requires efficient scattering so that the pitch-angle distribution of the accelerating electrons remains isotropic. We propose that the electrons undergo resonant scattering by high-frequency plasma R-waves that, as suggested by others (Hamilton & Petrosian 1992), are generated by the reconnection. Ions are not scattered by R-waves. Provided that there is negligible generation of ion-scattering plasma turbulence (e.g., L-waves) by the reconnection or the MHD turbulence, the ions will not Fermi-accelerate and the cascading energy is transferred only to the electrons. We conclude that, given this situation, electron Fermi acceleration can plausibly account for the electron bulk energization in impulsive solar flares.

Larosa, T. N.↗

NASA NTRS1984

Investigation of accelerated stress factors and failure/degradation mechanisms in terrestrial solar cells

Research on the reliability of terrestrial solar cells was performed to identify failure/degradation modes affecting solar cells and to relate these to basic physical, chemical, and metallurgical phenomena. Particular concerns addressed were the reliability attributes of individual single crystalline, polycrystalline, and amorphous thin film silicon cells. Results of subjecting different types of crystalline cells to the Clemson accelerated test schedule are given. Preliminary step stress results on one type of thin film amorphous silicon (a:Si) cell indicated that extraneous degradation modes were introduced above 140 C. Also described is development of measurement procedures which are applicable to the reliability testing of a:Si solar cells as well as an approach to achieving the necessary repeatability of fabricating a simulated a:Si reference cell from crystalline silicon photodiodes.

Lathrop, J. W.↗

NASA NTRS1999

Work on Planetary Atmospheres and Planetary Atmosphere Probes

A major objective of the grant was to complete the fabrication, test, and evaluation of the atmosphere structure experiment on the Galileo Probe, and to receive, analyze, and interpret data received from the spacecraft. The grantee was competitively selected to be Principal Investigator of Jupiter's atmosphere structure on the Galileo Probe. His primary motivation was to learn as much as possible about Jupiter's atmosphere by means of a successful atmosphere structure experiment, and to support the needs and schedule of the Galileo Project. After a number of launch delays, the Flight instrument was shipped to Kennedy Space Center 2 years after the start of this collaboration, on April 14, 1989, at which time it was determined from System level tests of the ASI on the Probe that the instrument was in good working order and ready for flight. The spacecraft was launched on October 18, 1989. Data analysis of test and calibration data taken over a period of years of instrument testing was continued in preparation for the encounter. The initial instrument checkout in space was performed on October 26, 1989. The data set received by telemetry was thoroughly analyzed, and a report of the findings was transmitted to the Probe Operations Office on Feb. 28, 1990. Key findings reported were that the accelerometer biases had shifted by less than 1 mg through launch and since calibration at Bell Aerospace in 1983; accelerometer scale factors, evaluated by means of calibration currents, fell on lines of variation with temperature established in laboratory calibrations; pressure sensor offsets, correlated as a function of temperature, fell generally within the limits of several years of ground test data; atmospheric and engineering temperature sensor data were internally consistent within a few tenths of a degree; and the instrument electronics performed all expected functions without any observable fault. Altogether, this checkout was highly encouraging of the prospects of instrument performance, although performed greater than 5 years prior to Jupiter encounter. Capability of decoding the science data from the Experiment Data Record to be provided at encounter was developed and exercised using the tape recording of the first Cruise Checkout data. A team effort was organized to program the selection and combination of data words defining pressure, temperature, acceleration, turbulence, and engineering quantities; to apply decalibration algorithms to convert readings from digital numbers to physical quantities; and to organize the data into a suitable printout. A paper on the Galileo Atmosphere Structure Instrument was written and submitted for publication in a special issue of Space Science Reviews. At the Journal editor's request, the grantee reviewed other Probe instrument papers submitted for this special issue. Calibration data were carefully taken for all experiment sensors and accumulated over a period of 10 years. The data were analyzed, fitted with algorithms, and summarized in a calibration report for use in analyzing and interpreting data returned from Jupiter's atmosphere. The sensors included were the primary science pressure, temperature, and acceleration sensors, and the supporting engineering temperature sensors. This report was distributed to experiment coinvestigators and the Probe Project Office.

Seiff, Alvin↗

NASA NTRS1984

Electron capture by U(91+) and U(92+) and ionization of U(90+) and U(91+)

U(92+)/U(91+) and U(91+)/U(90+) electron-capture and ionization cross sections and equilibrium charge-state distributions are measured experimentally in mylar, Cu and Ta of varying thickness. Relativistic U(68+) ions at 437 or 962 MeV/nucleon are produced by a heavy-ion linear accelerator and synchrotron in tandem and passed through the target material into a magnetic specrometer and position-sensitive proportional counter for evaluation of charge states. The results are presented graphically and discussed. At 962 MeV/nucleon, beams containing 85 percent bare U(92+) nuclei are obtained using 150-mg/sq cm Cu or 85-mg/sq cm Ta; at 437 MeV/nucleon, 50 percent bare U(92+) nuclei are obtained with 90-mg/sq cm Cu. The techniques decribed can be applied to produce beams of bare U nuclei for acceleration to ultrarelativistic speeds or beams of few-electron U for atomic-physics experiments on quantum electrodynamics.

Gould, H.↗

NASA NTRS1983

Plasma physics on auroral field lines - The formation of ion conic distributions

The formation of the conical distribution function and the acceleration of ions on aurora field lines are considered. Ion cyclotron waves were assumed to be excited by drifting electrons associated with the return current in the auroral zone. A theoretical analysis of ion cyclotron waves is given, and a simulation model is described. Simulation results are presented. The heating of ions and the evolution of ion cyclotron waves on auroral field lines and in the magnetosphere are discussed.

Ashour-Abdalla, M.↗

NASA NTRS1990

Composite materials for space applications

The objectives of the program were to: generate mechanical, thermal, and physical property test data for as-fabricated advanced materials; design and fabricate an accelerated thermal cycling chamber; and determine the effect of thermal cycling on thermomechanical properties and dimensional stability of composites. In the current program, extensive mechanical and thermophysical property tests of various organic matrix, metal matrix, glass matrix, and carbon-carbon composites were conducted, and a reliable database was constructed for spacecraft material selection. Material property results for the majority of the as-fabricated composites were consistent with the predicted values, providing a measure of consolidation integrity attained during fabrication. To determine the effect of thermal cycling on mechanical properties, microcracking, and thermal expansion behavior, approximately 500 composite specimens were exposed to 10,000 cycles between -150 and +150 F. These specimens were placed in a large (18 cu ft work space) thermal cycling chamber that was specially designed and fabricated to simulate one year low earth orbital (LEO) thermal cycling in 20 days. With this rate of thermal cycling, this is the largest thermal cycling unit in the country. Material property measurements of the thermal cycled organic matrix composite laminate specimens exhibited less than 24 percent decrease in strength, whereas, the remaining materials exhibited less than 8 percent decrease in strength. The thermal expansion response of each of the thermal cycled specimens revealed significant reduction in hysteresis and residual strain, and the average CTE values were close to the predicted values.

Rawal, Suraj P.↗

NASA NTRS1991

Electron beams and associated rapid fluctuations in solar flares

Recent observations show that the rapid fluctuations in radio, hard X-ray, and H-alpha emissions are closely associated with type III and microwave (or decimetric) bursts during the impulsive and/or preimpulsive phases of solar flares. In order to clarify the physical processes of these observed phenomena, this paper proposes a tentative model of two acceleration regions A (source of type III bursts) and B (source of microwave or decimetric bursts) formed in the neutral sheet and at the top of a flaring loop, respectively; and also suggests that the electron beams streaming from region A and/or region B downward to the chromosphere are responsible for the rapid fluctuations in the different emissions mentioned above during the impulsive and/or preimpulsive phases of solar flares.

Li, C. S.↗

NASA NTRS1990

The goals of gamma-ray spectroscopy in high energy astrophysics

The use of high resolution gamma-ray spectroscopy in astrophysics is discussed with specific attention given to the application of the Nuclear Astrophysics Explorer (NAE). The gamma-ray lines from nuclear transitions in radionucleic decay and positron annihilation permits the study of current sites, rates and models of nucleosynthesis, and galactic structure. Diffuse galactic emission is discussed, and the high-resolution observations of gamma-ray lines from discrete sites are also described. Interstellar mixing and elemental abundances can also be inferred from high-resolution gamma-ray spectroscopy of nucleosynthetic products. Compact objects can also be examined by means of gamma-ray emissions, allowing better understanding of neutron stars and the accreting black hole near the galactic center. Solar physics can also be investigated by examining such features as solar-flare particle acceleration and atmospheric abundances.

Lingenfelter, Richard E.↗

NASA NTRS1992

INSPIRE - Premission

The Interactive NASA Space Physics Ionosphere Radio Experiment (INSPIRE) designed to assist in a Space Experiments with Particle Accelerators (SEPAC) project is discussed. INSPIRE is aimed at recording data from a large number of receivers on the ground to determine the exact propagation paths and absorption of radio waves at frequencies between 50 Hz and 7 kHz. It is indicated how to participate in the experiment that will involve high school classes, colleges, and amateur radio operators.

Taylor, William W. L.↗

NASA NTRS1994

Comparison of the plasma tails of four comets: P/Halley, Okazaki-Levy-Rudenko, Austin, and Levy

Photographic and charge coupled device (CCD) plasma tail observations are compared for four comets: P/Halley (22 nights in 1985/1986), Okazaki-Levy-Rudenko 1989 XIX (1989 December 2), Austin 1990 V (nine nights in 1990), and Levy 1990 XX (two nights in 1991). We present a discussion of several image-processing techniques used to enhance the visibility of the plasma tail features in order to measure velocities, accelerations, and position angles. The data are used to assess the validity of various physical mechanisms proposed to explain plasma tail phenomena. Seven disconnection events were observed in the comet P/Halley data, two in the Austin data, and none for the other comets. Analysis of these data suggests that while the crossing of the solar neutral sheet (the sector boundary) is a prominent factor in the production of a disconnection event, it is likely that several mechanisms are at work. A sector boundary crossing has been ruled out as the cause of either the 1986 April 26 P/Halley disconnection or the 1990 May 5/6 Austin disconnection. The motions of the disconnection events, knots, and condensations in the tails were seen to increase from 30-60 km/s near the nucleus (within 10(exp 6) km) to 80-100 km/s at 10(exp 7) km, consistent with either bulk motion or Alfven waves. Distinguishing between the two cases is not possible with these data. It was found that although the tail ray rotation rate slows as the ray approaches the tail axis, it is not a good indicator of the solar wind speed. Historical plasma tail data are also used to look for clues as to why some comets form well-developed plasma tails and others do not.

Farnham, Tony L.↗

NASA NTRS2004

To Boldly Go: America's Next Era in Space. The Plasma Universe

Dr. France Cordova, NASA's Chief Scientist, chaired this, the eighth seminar in the Administrator's Seminar Series. She introduced the NASA Administrator, Daniel S. Goldin, who, in turn, introduced the subject of plasma. Plasma, an ionized gas, is a function of temperature and density. We ve learned that, at Jupiter, the radiation is dense. But, Goldin asked, what else do we know? Dr. Cordova then introduced Dr. James Van Allen, for whom the Van Allen radiation belt was named. Dr. Van Allen, a member of the University of Iowa faculty, discussed the growing interest in practical applications of space physics, including radiation fields and particles, plasmas and ionospheres. He listed a hierarchy of magnetic fields, beginning at the top, as pulsars, the Sun, planets, interplanetary medium, and interstellar medium. He pointed out that we have investigated eight of the nine known planets,. He listed three basic energy sources as 1) kinetic energy from flowing plasma such as constitutional solar wind or interstellar wind; 2) rotational energy of the planet, and 3) orbital energy of satellites. He believes there are seven sources of energetic particles and five potential places where particles may go. The next speaker, Dr. Ian Axford of New Zealand, has been associated with the Max Planck Institut fuer Aeronomie and plasma physics. He has studied solar and galactic winds and clusters of galaxies of which there are several thousand. He believes that the solar wind temperature is in the millions of degrees. The final speaker was Dr. Roger Blanford of the California Institute of Technology. He classified extreme plasmas as lab plasmas and cosmic plasmas. Cosmic plasmas are from supernovae remnants. These have supplied us with heavy elements and may come via a shock front of 10(sup 15) electron volts. To understand the physics of plasma, one must learn about x-rays, the maximum energy of acceleration by supernova remnants, particle acceleration and composition of cosmic rays, maximum acceleration, and how fast protons are heated by ions. He asked questions about where high energy cosmic rays are made, what accelerates electrons, radiates gamma rays, makes electronpositron plasma, and finally noted that pulsars are good time keepers, but we need a better understanding of their mechanism and of plasmas, both cosmic and ground-based. In the discussion period, Goldin asked if NASA should put up an x-ray interferometer. The answer was no; gamma rays are of greater interest just now. Goldin also asked what the assembled scientists would like to see for a future mission? They expressed an interest in learning more about the origin of galaxies, cosmic rays, solar systems, planets, the existence of life "out there", gamma ray sources, the nature of gamma ray bursts, and the flow of gases around black holes. The discussion concluded with a suggestion that NASA should communicate to the general public more information regarding actual technological trials and tribulations involved in getting an experiment to work. The speakers thought that this would help non-scientists to better appreciate what it is that NASA does in connection with the benefits that are achieved.

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NASA NTRS2008

Nanophase Nickel-Zirconium Alloys for Fuel Cells

Nanophase nickel-zirconium alloys have been investigated for use as electrically conductive coatings and catalyst supports in fuel cells. Heretofore, noble metals have been used because they resist corrosion in the harsh, acidic fuel cell interior environments. However, the high cost of noble metals has prompted a search for less-costly substitutes. Nickel-zirconium alloys belong to a class of base metal alloys formed from transition elements of widely different d-electron configurations. These alloys generally exhibit unique physical, chemical, and metallurgical properties that can include corrosion resistance. Inasmuch as corrosion is accelerated by free-energy differences between bulk material and grain boundaries, it was conjectured that amorphous (glassy) and nanophase forms of these alloys could offer the desired corrosion resistance. For experiments to test the conjecture, thin alloy films containing various proportions of nickel and zirconium were deposited by magnetron and radiofrequency co-sputtering of nickel and zirconium. The results of x-ray diffraction studies of the deposited films suggested that the films had a nanophase and nearly amorphous character.

Narayanan, Sekharipuram↗

NASA NTRS1997

Ion-Atom Cold Collisions and Atomic Clocks

Collisions between ultracold neutral atoms have for some time been the subject of investigation, initially with hydrogen and more recently with laser cooled alkali atoms. Advances in laser cooling and trapping of neutral atoms in a Magneto-Optic Trap (MOT) have made cold atoms available as the starting point for many laser cooled atomic physics investigations. The most spectacularly successful of these, the observation of Bose-Einstein Condensation (BEC) in a dilute ultra-cold spin polarized atomic vapor, has accelerated the study of cold collisions. Experimental and theoretical studies of BEC and the long range interaction between cold alkali atoms is at the boundary of atomic and low temperature physics. Such studies have been difficult and would not have been possible without the development and advancement of laser cooling and trapping of neutral atoms. By contrast, ion-atom interactions at low temperature, also very difficult to study prior to modern day laser cooling, have remained largely unexplored. But now, many laboratories worldwide have almost routine access to cold neutral atoms. The combined technologies of ion trapping, together with laser cooling of neutrals has made these studies experimentally feasible and several very important, novel applications might come out of such investigations . This paper is an investigation of ion-atom interactions in the cold and ultra-cold temperature regime. Some of the collisional ion-atom interactions present at room temperature are very much reduced in the low temperature regime. Reaction rates for charge transfer between unlike atoms, A + B(+) approaches A(+) + B, are expected to fall rapidly with temperature, approximately as T(sup 5/2). Thus, cold mixtures of atoms and ions are expected to coexist for very long times, unlike room temperature mixtures of the same ion-atom combination. Thus, it seems feasible to cool ions via collisions with laser cooled atoms. Many of the conventional collisional interactions, exploited as a useful tool at room temperature and higher, are greatly enhanced at low energy. For example, collisional spin transfer from one species of polarized atoms to another has long been a useful method for polarizing a sample of atoms where no other means was available. Because optical pumping cannot be used to polarize the nuclear spin of Xe-129 or He-3 (for use in nmr imaging of the lungs), the nuclear spins are polarized via collisions with an optically pumped Rb vapor in a cell containing both gases. In another case, a spin polarized thermal Cs beam was used to polarize the hyperfine states of trapped He(+)-3 ions in order to measure their hyperfine clock transition frequency. The absence of an x-ray light source to optically pump the ground state of the He(+)-3 ion necessitated this alternative state preparation. Similarly, Cd(+) and Sr(+) ions were spin-oriented via collisions in a cell with optically pumped Rb vapor. Resonant RF spin changing transitions in the ground state of the ions were detected by changes in the Rb resonance light absorption. Because cold collision spin exchange rates scale with temperature as T(sup -1/2) this technique is expected to be a far more powerful tool than the room temperature counterpart. This factor of 100 or more enhancement in spin exchange reaction rates at low temperatures is the basis for a novel trapped ion clock where laser cooled neutrals will cool, state select and monitor the ion clock transition. The advantage over conventional direct laser cooling of trapped ions is that the very expensive and cumbersome UV laser light sources, required to excite the ionic cooling transition, are effectively replaced by simple diode lasers.

Prestage, John D.↗

NASA NTRS1986

Signatures of current loop coalescence in solar flares

The nonlinear coalescence instability of current carrying solar loops can explain many of the characteristics of the solar flares such as their impulsive nature, heating and high energy particle acceleration, amplitude oscillations of electromagnetic emission as well as the characteristics of 2-D microwave images obtained during a solar flare. The physical characteristics of the explosive coalescence of currents are presented in detail through computer simulation and theory. Canonical characteristics of the explosive coalescence are: (1) a large amount of impulsive increase of kinetic energies of electrons and ions; (2) simultaneous heating and acceleration of electrons and ions in high and low energy spectra; (3) ensuing quasi-periodic amplitude oscillations in fields and particle quantities; and (4) the double peak (or triple peak) structure in these profiles, participate in the coalescence process, yielding varieties of phenomena.

Sakai, J.↗